TRANSLATING WORDS INTO ALGEBRAIC EXPRESSIONS!
Summary
TLDRThis lesson focuses on translating written expressions and equations into algebraic form using numbers and variables. The video explains key terms like 'sum,' 'more than,' 'less than,' and 'product,' demonstrating how to represent these mathematically. It highlights the importance of variables, parentheses, and switch words like 'then' in translation. Through examples, viewers learn to convert phrases such as '10 plus a number' and 'the difference of six and a number' into numerical expressions. The video concludes with a lighthearted math joke and encourages viewers to practice for better understanding.
Takeaways
- 📚 The lesson focuses on translating written algebraic expressions and equations into numerical form using variables.
- ❓ Variables like 'X' represent unknown values, and the letter used is interchangeable with any alphabet letter.
- ➕ Addition expressions like '10 plus a number' translate to '10 + X', where 'X' is the variable.
- 🔄 For phrases like '10 more than a number', the order changes, and the translation becomes 'X + 10'.
- ➖ When subtraction is involved, such as in '6 less than a number', the translation switches to 'X - 6'. The word 'then' signals a switch in order.
- ✂️ Subtraction examples, like 'the difference of 3 and a number', translate to '3 - X'. Complex expressions may need parentheses.
- ➗ Division, such as 'a number divided by 3 is 8', translates to 'X / 3 = 8', with 'is' representing equals.
- ✖️ The product of numbers or variables, like 'the product of a number and 9', translates to '9 * X' or '9X'.
- ➗ Expressions like 'half a number decreased by 12' are represented as 'X / 2 - 12'.
- 🏁 The lesson concludes with a reminder to practice translating phrases into algebraic expressions and equations for better understanding.
Q & A
What is the primary goal of this algebraic translation lesson?
-The primary goal of the lesson is to teach students how to translate written expressions and equations into numerical form using numbers and variables.
How would you translate '10 plus a number' into an algebraic expression?
-'10 plus a number' translates to the algebraic expression 10 + x, where x represents an unknown number.
How does the phrase '10 more than a number' differ from '10 plus a number' in algebraic terms?
-'10 more than a number' translates to x + 10, where the variable comes first. While both involve addition, 'more than' suggests the number comes before the 10.
How do you interpret the phrase '6 less than a number' algebraically?
-'6 less than a number' translates to n - 6. The phrase uses 'less than,' which means subtraction, and the order is reversed, with the variable coming before the 6.
What does the word 'then' signal in an algebraic translation?
-The word 'then' signals a switch in the order of terms. In expressions like '6 less than a number,' it indicates that the second term (the variable) comes before the first term (6).
How would you translate 'the difference of three and a number'?
-'The difference of three and a number' translates to 3 - p, where the word 'difference' indicates subtraction and 'p' represents the unknown number.
How should you handle parentheses when performing algebraic translations?
-Parentheses are used to separate independent groupings in algebraic translations, especially when multiple operations are involved. For example, 'the difference of a number and twice a number plus one' would be written as n - (2p + 1).
What does the word 'is' signify in algebraic expressions?
-In algebraic expressions, the word 'is' signifies equality and is represented by the equal sign (=). For example, 'a number divided by 3 is 8' would be written as t/3 = 8.
How do you translate 'three times the difference of a number and one'?
-'Three times the difference of a number and one' translates to 3 * (p - 1), where the expression inside the parentheses (p - 1) represents the difference, and it's multiplied by 3.
How do you translate '20 times a number less than two'?
-'20 times a number less than two' translates to 2 - 20y. The word 'less than' indicates subtraction, and since 'then' is a switch word, the order of the terms is reversed.
Outlines
🔢 Introduction to Algebraic Translation
This paragraph introduces the lesson on translating written expressions and equations into numerical form. The focus is on recognizing and converting verbal statements into algebraic expressions. It starts with simple examples, like '7 + 5' being described as 'the sum of seven and five.' The explanation then introduces variables, such as using 'X' to represent unknown numbers, and emphasizes that any letter can function as a variable in algebra.
➕ Translating 'More Than' and 'Less Than'
This paragraph focuses on understanding how to translate expressions involving addition and subtraction, especially with phrases like '10 more than a number' and 'six less than a number.' It highlights the importance of recognizing the 'switch word' concept, where the order of terms is reversed in expressions involving 'then,' such as in subtraction ('six less than a number' becomes 'number - 6').
➖ Differences and Grouping
Here, the lesson dives deeper into more complex phrases like 'the difference of three and a number' and expressions involving more than one operation, like 'the difference of twice a number and one.' The key concept introduced is using parentheses to group expressions and maintain the correct order of operations. Examples highlight how parentheses clarify groupings when translating verbal phrases into algebraic expressions.
➗ Division and Equality in Algebraic Translation
The focus shifts to translating phrases involving division and equality, such as 'a number divided by 3 is 8.' It explains that 'is' represents equality ('='), while divisions are often represented as fractions. The paragraph recaps the importance of recognizing key terms, such as 'a number' (which means a variable), and understanding how to structure algebraic equations correctly.
✖️ Translating Products and Complex Phrases
This paragraph introduces more examples, such as translating 'the product of a number and nine' into algebraic form. It explains the common convention of writing multiplication without the multiplication symbol (e.g., 9n instead of 9 * n). More complex phrases, like 'three times the difference of a number and one,' are also discussed, again emphasizing the importance of parentheses to maintain proper grouping in algebraic expressions.
🧮 Handling 'Less Than' and Complex Equations
This section provides examples of translating phrases like '20 times a number less than two' and introduces how to handle more intricate operations. The phrase 'less than' is shown to be a switch word, requiring the order of terms to be reversed. Another example translates a phrase involving the sum of five and the square root of eight times a number into an equation, stressing the importance of identifying when a phrase should result in an equation rather than just an expression.
📝 Conclusion and Recap of Key Concepts
The lesson concludes by recapping key ideas, such as recognizing variables, understanding the 'switch word' concept, using parentheses for grouping, and equating 'is' to '=' in algebraic expressions. The paragraph encourages practice, stating that repetition will make these concepts easier to grasp. It ends with a light-hearted joke to close the lesson on a fun note, followed by a call to engage with the team on social media.
Mindmap
Keywords
💡Algebraic Translation
💡Variable
💡Addition
💡Subtraction
💡Switch Word
💡Parentheses
💡Multiplication
💡Division
💡Equation
💡Commutative Property
Highlights
Introduction to algebraic translation: converting written expressions into numerical form.
Basic concept: replacing variables with letters (commonly X) to represent unknown values in expressions.
Example: translating '10 plus a number' into the algebraic form '10 + X'.
Addition rule: order doesn't matter in addition due to its commutative property.
Subtraction example: 'six less than a number' is expressed as 'N - 6' where the order is reversed.
'Then' as a switch word: it indicates that the order of terms must be reversed when forming expressions.
Example: 'the difference of three and a number' translates to '3 - P'.
More complex example: 'the difference of and twice a number + 1' becomes '3 - (2P + 1)' with parentheses separating groupings.
Using parentheses to handle independent groupings when translating complex expressions.
Division example: 'a number divided by 3 is 8' translates to 'T/3 = 8'.
Is/equivalent means equals: translating statements with 'is' to the equals sign in algebraic form.
Multiplication example: 'the product of a number and nine' translates to '9N' without the multiplication sign.
Expression: 'half a number decreased by 12' is translated into 'X/2 - 12'.
Handling multiple terms: 'three times the difference of a number and one' translates to '3 * (P - 1)'.
Final example: translating 'the sum of five and the square of 8 times a number is 12' to '5 + √(8R) = 12'.
Transcripts
[Music]
hello everyone and welcome to this
lesson on algebraic
translation now our aim for this lesson
is how can we translate written
expressions and equations into numerical
form so basically we see it in written
form and we want to write it in terms of
numbers and
variables now before we can do that we
have to lay the groundwork here and
there's a few things that we need to
know so that we can use them when we get
to doing the actual
translations now if we had something
like 7 + 5 verbally we could express
this for example as the sum of seven and
five and we would be done but what if
instead of a seven we had a variable we
had the letter X there instead of saying
the sum of seven and five we would say
the sum of a number and five because X
is a variable and it could represent any
number so we're just going to call it a
number and even though X is the most
commonly used letter this applies to any
letter in the alphabet that can be used
to represent a variable which is just
some unknown
value so let's
translate 10 plus a number so again it's
an expression so we have the number 10
plus we know is just addition and then a
number is just some unknown we'll call
it X so that translates to 10 + x
now what if we add the statement 10 more
than a number now we should know that
more than is associated with addition so
our sign is not going to change so let's
think about this one differently we have
a number some unknown number some
variable and this phrase represents 10
more than whatever that number is so in
this case we're going to start with the
variable and then add 10 to it now since
this was addition and because addition
is commutative the order didn't actually
matter but let's take a look at an
example Now using
subtraction so now let's look at six
less than a number so again we see that
word then so we have three parts here we
have the number six we have less than
which we know is subtraction and then a
number we'll call it n now this phrase
represents a value that is six units
smaller than whatever our number n is so
to find that number we would have to
take n and subtract six from
it so in cases like this the second term
comes first and the first term comes
second we have to switch the
order now this is the case when we see
the word then and we're going to say
that then is a switch word which means
that the operator stays in the middle
but the order of the first term and the
last term is Switched so the way that
it's written the actual expression will
be in reverse order cool moving on now
if we had the phrase the difference of
three and the number we could easily
translate this difference is subtraction
and we have three minus some number
we'll call it P so 3 minus P would
represent this
phrase but what if instead of the
difference of three and a number we had
the difference of end twice a number +
one so now instead of P we have to
represent that whole expression which we
can call 2 p +
1 and we can enclose this individual
expression in
parentheses so when performing algebraic
translations you can use parentheses to
separate independent
[Music]
groupings and now let's look at a number
divided 3
is
8 so we have a number let's call it t
and we're dividing it by three so let's
use it as a fraction T over3 and when we
say is 8 that just means that it equals
8 so be aware that the word is or is
equivalent to just means equals
to so a quick recap before we get into
the examples remember that a number is
just a variable the word then we call a
switch word use parentheses for
independent groupings and is means equal
to so now we're ready for a few examples
so first let's translate the phrase the
product of a number and nine so we know
that product just means to
multiply and what we're multiplying
together is a number we'll call it n and
the number 9 now n * 9 is fine but we'll
more commonly see it written as 9 N
without the multiplication sign but that
means 9 *
n next we have the phrase half a number
decreased by 12 decrease by means to
subtract and now the first term is half
a number we'll call that number X and
half of it means dividing it by two so
we have X over 2 - 12 so that expression
is the translation of that verbal phrase
next we want to translate the phrase
three times the difference of a number
and
one so basically we're multiplying three
by another expression whatever the
difference of a number and one is so you
have two separate parts here so we have
three multiplied by an independent group
in this case the difference of a number
in one which we'll call P minus
one so this is an example of how you can
use parentheses to separate independent
groupings and if you don't use the
parentheses here it will not be
[Music]
correct our next example is 20 times a
number less than two so we have three
parts here we have 20 times a number
less than and
two notice the phrase less than we know
that less than means subtraction
we need to remember that then is a
switch word so we're going to switch the
order of the
terms so our translation is going to be
the value of
2 minus 20 times a number which we can
call 20 y so our translation will be 2us
20
y okay and for our last example we have
the sum of five and the Square < TK of 8
* a number is
12 we know that sum means addition so
we're going to need a plus sign and we
are basically adding two terms together
and that is going to be equal to some
other value so we just have to plug in
here now so 5 plus the square root of 8
times a number we'll call it 8 R is
equal to 12 remember that is just means
equal to and now we have translated this
phrase into an algebraic
equation not an expression remember
equations have an equal sign so that's
it for this lesson I know that we
explored a lot in this one so you
probably want to go back and redo those
examples again remember practice makes
perfect the more you go through them the
more you think about these Concepts the
better you'll understand them and the
easier it will become so I'll leave you
guys off with a joke what does a nosy
pepper do get jalapeno
business sorry guys I'll see you next
time thank you again everyone for
joining us and please reach out to us on
Twitter at mashup maath we are dying to
hear from you so please share some love
all right we're done here
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